Interviews with (n=20) primary teachers, who had participated in inservice workshops on Cognitively Guided Instruction (CGI), revealed three patterns of CGI use--as mainstay, as supplement, and decreasingly--which seemed related to their beliefs about mathematics, learning, and CGI itself. (40 references) (MKR)

This study investigated the propositions that (1) the expressed preference for formal-deductive style of thinking and mathematics anxiety are negatively correlated; (2) the preferred cognitive style is positively correlated with the respondent's self-assessment of mathematical ability; and (3) those expressing a preference for the analyst style of…

Reviews research indicating that students' cognitive models hold random events to be equiprobable Examined 87 students between the ages of 15 and 17 to determine whether masking a random event using geometric figures would affect the students' view of the event as equiprobable. Results indicated that masking overcame the equiprobable bias of the…

A mapping procedure based on the SOLO Taxonomy developmental model was used to classify the problem-solving strategies of students (n=34) in grades K-2. Only one multiplication problem was used to isolate three components of the problem-solving procedure. (MDH)

The facets of teachers' views of mathematics include their personal views, how they view mathematics for their students, how they view the mathematics curriculum, and how they view mathematics teaching. This paper reports a pilot study to examine how elementary school teachers view mathematics both personally and for their students. A coding…

Recent contributions from theory, research, and practice in second-language instruction are discussed in relation to mathematics education. Three methods of teaching and learning second languages are described--"Delayed Oral Production," the "Silent Way," and the "Counseling Learning/Community Language Learning." (KR)

Discussed are preservice elementary teachers' misconceptions and inconsistent beliefs about multiplication and division with decimals. Sources of inconsistencies and recommendations for overcoming inconsistencies are included. (KR)

This study examines the construct of problem representation and the processes used by learners to construct or modify problem representations in problem-solving situations. Students (n=14) from freshman calculus courses at the University of California at San Diego participated in videotaped interviews in which they were asked to think aloud as…

This study focuses on the possible relationships between cognitive preference scores of algebra students and level of algebra, sex, and performance rank in algebra classes. The sample consisted of 162 students from a high school in the Denver area. The instruments used were the Cognitive Preference Test: Mathematics (Revised) (CPTM) and the…

Interviews with 72 mixed ability students, aged 7 to 12, about arithmetic problem-solving strategies, indicated that the preference between procedural and deductive strategies becomes a divergent reality across ability levels. Among the conclusions is that more able children tend to be doing a qualitatively different sort of mathematics than their…

Discusses dilemmas teachers may face when shifting their concept of teaching or tutoring from explaining or telling to a constructivist perspective of facilitating the development of students' knowledge structures. Examines teachers' decisions during a 20-minute segment of dialogue between a student and teacher while studying linear functions. (14…

This document reports on a study into the relationships between cognitive preferences, achievement, and ethnicity of first year algebra students. The sample consisted of 175 students from two high schools in the Denver (Colorado) metropolitan area. The two schools were chosen because of the diversity of ethnic groups in the student populations.…

Discussed are inconsistencies and cognitive conflict with respect to current mathematical knowledge of students and how that knowledge might be modified is discussed. The inconsistencies that students generate for themselves and those produced by the teacher are described. (KR)

Discussed are the issues of inconsistencies and compartmentalization and the use of inconsistencies in the classroom. Included are discussions on paradoxes, the naive student, logical reasoning ability, and the development of the students' cognitive structures. (KR)

Discusses a system of classification for students' inconsistent ideas in mathematics, the sources of students' mathematical inconsistency, and instructional strategies for helping students to resolve apparent learning inconsistencies. Language, curriculum, and instruction are included in the discussion. (KR)